1. Trying to figure out this word problem. Its two people are painting a fence. One person can paint a fence in 6 hours, the second can paint it in 8 hours. After two hours, the first goes fishing and leaves the second to finish the fence. How long does it take the second to finish the fence?

x -----x
- + - = 1
6 -----8

Turns out to be

--20
2 -
--14
To finish the entire fence together.

Now this is where I am stuck. I assume you take away the 2 (which equates to hours) which leaves 20 over 14 but what do you do after that?

Thanks for the help.

2.

3. I didn't really understand your notation, but:
The first person is painting at 1/6 of a fence per hour. The second at 1/8 of a fence per hour. The first person paints 1/6 of a fence per hour times 2 hours. The second person paints 1/8 of a fence times 2+x hours. In sum they paint one fence. so
(1/6)*2+(1/8 )*(2+x)=1
Solve for x.

4. Thanks Harold. Is the answer 3 and 1/3rd hours to finish painting the fence? (So the fence would take 5 and 1/3rd hours total to paint.)

5. Originally Posted by verzen
Thanks Harold. Is the answer 3 and 1/3rd hours to finish painting the fence? (So the fence would take 5 and 1/3rd hours total to paint.)
Yes, that's what I get.

6. Take the sum of the percent (as a decimal) of how much they can paint in an hour. This would be the equivalent of , now multiply by how long they work before person number one stops, which would be . Now we know that the fence has been requires of his total percentage left to paint. We divided five over twelve now by the rate of how long person two can work, which is one-eigth of the total fence, which would be . Therefore, person two would have to work for a remaining three and one-third hours to paint the fence, and they took five and one-third hours in total.

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